feat(stats): best-move word, moves & hint-share, and a hint-count fix (#81)

The statistics screen gains real depth, plus a hint-count bug fix found along the way.

- Best move per variant: the screen shows the actual best-move word (drawn as game
  tiles; a wildcard shows its letter but no value), broken down by game variant, empty
  variants omitted. New account_best_move table, written at game finish.
- Moves & hint share: two new lifetime tiles — the player's play count and the share of
  plays that used a hint — from summed account_stats counters (moves, hints_used).
  Honest-AI games are excluded, like the rest of the stats.
- Hint-count fix: the in-game hint badge no longer goes stale across games. The global
  wallet now rides the wire apart from the per-game allowance (wallet_balance on
  StateView/HintResult/StatsView), so the client reads the live wallet rather than a
  per-game snapshot; game_players.hints_used now counts every hint (allowance + wallet),
  its true per-game total.
- Account merge: sums the new moves/hints_used counters and merges the per-variant best
  moves (higher score kept), which it previously dropped.
- Admin: the user card shows Moves and Hints used.
- UI polish: tab/label wording, game-over text, and e2e selectors hardened against label
  changes.

All wire additions are trailing (backward-compatible). Docs (ARCHITECTURE, FUNCTIONAL +ru,
UISN_DESIGN) updated in step.

ui/e2e/quickmatch.spec.ts

@@ -8,7 +8,7 @@ import { expect, test } from './fixtures';
 test('quick game: enter immediately, wait for an opponent, then it joins', async ({ page }) => {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
-  await page.getByRole('button', { name: /New/ }).click(); // lobby tab bar -> auto-match
+  await page.getByRole('button', { name: /🎲/ }).click(); // lobby tab bar -> auto-match
 
   // Choose a random human opponent (the default is the AI); pick a variant and start. The player
   // lands in an open game at once (no "searching" screen).
@@ -38,7 +38,7 @@ test('quick game: enter immediately, wait for an opponent, then it joins', async
 test('AI game: 🤖 opponent, no wait, chat disabled, dictionary still works', async ({ page }) => {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
-  await page.getByRole('button', { name: /New/ }).click();
+  await page.getByRole('button', { name: /🎲/ }).click();
 
   // AI is the default opponent: the move-clock line is replaced by the 7-day inactivity rule.
   await expect(page.getByText(/Loss after 7 days of inactivity/)).toBeVisible();
@@ -64,7 +64,7 @@ test('AI game: 🤖 opponent, no wait, chat disabled, dictionary still works', a
 test('AI game: no GCG export offered after it ends', async ({ page }) => {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
-  await page.getByRole('button', { name: /New/ }).click();
+  await page.getByRole('button', { name: /🎲/ }).click();
   await page.locator('.variant').first().click(); // AI is the default opponent
   await page.getByRole('button', { name: /Start game/i }).click();
   await expect(page.locator('.scoreboard').getByText('🤖')).toBeVisible();
@@ -90,7 +90,7 @@ test('AI game: no GCG export offered after it ends', async ({ page }) => {
 async function enterOpenGame(page: import('@playwright/test').Page): Promise<void> {
   await page.goto('/');
   await page.getByRole('button', { name: /guest/i }).click();
-  await page.getByRole('button', { name: /New/ }).click();
+  await page.getByRole('button', { name: /🎲/ }).click();
   await page.getByRole('button', { name: 'Random player' }).click();
   await page.locator('.variant').first().click();
   await page.getByRole('button', { name: /Start game/i }).click();